Chapter A.1, Problem 66E

Solution

Simplify the radical expression.

  $\frac{4y^4}{z^4}$ .

Given:

The given expression is $\sqrt{16y^8{z}^{-8}}$ .

Concept Used:

• Find the largest factor in the radicand that is a perfect power of the index. Rewrite the radicand as a product of two factors, using that factor.
• Use the product rule to rewrite the radical as the product of two radicals.
• Simplify the root of the perfect power.

Calculation:

The given expression is $\sqrt{16y^8{z}^{-8}}$ .

  $\begin{array}{c}\sqrt{16y^8{z}^{-8}}=\sqrt{\frac{16y^8}{z^8}}\\ =\sqrt{\frac{{(4)}^2{(y^4)}^2}{{(z^4)}^2}}\\ =\frac{4y^4}{z^4}\end{array}$

Thus after simplifying $\sqrt{16y^8{z}^{-8}}$ we get $\frac{4y^4}{z^4}$ .